一类高分数阶微分方程的积分边值问题的正解

Positive solution to integral boundary value problem for a class of higher fractional differential equation

本文利用锥拉伸和压缩不动点定理研究了一类高分数阶微分方程的积分边值问题,获得了相应的格林函数及其性质,同时将该问题转化为等价的积分算子方程,结合全连续算子的性质,在超线性和次线性条件下给出了方程至少有一个和至少有两个正解的充分条件.

By using fixed point theory of cone expansion and compression of norm type,a class of boundary value problem for higher fractional differential equation with integral conditions is investigated.The relevant Green function and its property is obtained.At the same time,the problem has beem reduced to the epuivalent integral opertor epuation.Combined with the properties of completely continuous maps,some sufficient conditions on the existence of at least one and two positive solutions are established under superlinear and sublinear conditions.